In our simplified physical picture thus far, the critical energies \(E^c_n\)  are identified as the Riemann zeros \(t_n\)  based on (REF ).
Whereas the quantization \(n\)  in (REF ) is robust, i.e. sample independent due to its relation to the Chern topological number,
the values at the transition \(E^c_n\)  are not universal. They depend in particular on the realization of the disorder, i.e. details of the
disorder, among other properties of the sample.
A famous conjecture is that the differences between Riemann zeros \(t_n\)  satisfies the GUE statistics of random hamiltonians [1]}, [2]}. In the present context this randomness is naturally explained as arising from the random disorder.
In fact random matrix theory has already been applied to quantum transport in disordered systems [3]}.
The actual Riemann zeros must then correspond to a special realization of disorder, just as the Hilbert-Pólya idea involves some as yet unknown hamiltonian.
It is important then that our formula (REF ) can be deformed in order to accommodate for variable
\(E^c_n \ne t_n\) , and other variations such as finite temperature. This will be explored in Section IV.
It is interesting to note that extreme values of \(|\zeta ( \tfrac{1}{2}+ i t)|\)  were studied from the perspective of the so-called freezing transition in disordered landscapes [4]}, [5]}, and the latter is an important component of the physics of the IQHE.
